Nonstick vegetable oil spray
2 1/2 cups all-purpose flour
2 teaspoons baking powder
1 1/2 teaspoons kosher salt
3/4 teaspoon baking soda
1 teaspoon ground cinnamon
1 teaspoon ground ginger
1 pound carrots, peeled, coarsely grated
1 cup buttermilk, room temperature
4 large eggs, room temperature
1 cup granulated sugar
3/4 cup (packed) dark brown sugar
2 teaspoons vanilla extract
3/4 cup vegetable oil
Classic Cream Cheese Frosting
1 cup unsweetened coconut flakes
Special Equipment: 2 (9") round cake pans
Position rack in center of oven; preheat to 350°F. Spread shredded coconut in a single layer on a rimmed baking sheet and toast until golden brown and aromatic, 3–5 minutes. Let cool 5 minutes. Meanwhile, lightly coat cake pans with nonstick spray. Line bottom of pans with parchment paper; lightly coat parchment with nonstick spray. Whisk toasted coconut, flour, baking powder, salt, baking soda, cinnamon, and ginger in a medium bowl. Combine carrots and buttermilk in another medium bowl. Using an electric mixer on high speed, beat eggs, granulated sugar, brown sugar, and vanilla in a large bowl until pale and thick, about 4 minutes. Reduce speed to medium-low and gradually stream in oil. Add dry ingredients in 3 additions, alternating with carrot mixture in 2 additions, beginning and ending with dry ingredients; beat until smooth. Divide batter between prepared pans; smooth top. Bake cakes, rotating pans halfway through, until a tester inserted into the center comes out clean, 40–45 minutes. Transfer pans to a wire rack and let cakes cool 10 minutes. Run a knife around sides of cakes and invert onto wire rack; remove parchment. Let cool completely. Spread 1 Tbsp. frosting in the center of a platter. Place 1 cake, domed side down, on platter. Spread 1 1/4 cups frosting evenly over top. Place remaining cake, domed side down, on top. Spread top and sides with 2 cups frosting. Chill 30 minutes to let frosting set. Spread remaining frosting over top and sides of cake, swirling top decoratively. Press coconut flakes into frosting on sides of cake. Chill at least 30 minutes or up to overnight to let frosting set.